Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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When does a linear graph represent a proportional relationship?

When it is vertical
When it does not pass through the origin
When it has a slope that is not zero
When it passes through the origin

The correct answer is: When it passes through the origin

A linear graph represents a proportional relationship when it passes through the origin. This is because a proportional relationship can be defined as one where two quantities maintain a constant ratio, indicating that when one quantity is zero, the other must also be zero. In graphical terms, this is represented as the line passing through the point (0,0), which signifies that when the independent variable (x) is zero, the dependent variable (y) is also zero. Consequently, the relationship can be described with a linear equation of the form y = kx, where k is a constant representing the slope. This means for any value of x, the value of y will change proportionally based on that constant. While a line with a non-zero slope can indicate a relationship, it must also cross the origin to be considered proportional. If it were to not pass through the origin, it would suggest that there is some constant value added or subtracted, indicating a different form of relationship rather than a proportional one. Specifically, a vertical line does not represent a function at all, and thus cannot indicate proportionality, while a line with a slope of zero represents a constant relationship, not a proportional one.